Sectional category of subgroup inclusions and sequential topological complexities of aspherical spaces as A-genus

TL;DR

This paper characterizes the sectional category of subgroup inclusions and sequential topological complexities of aspherical spaces using the A-genus, providing new insights into group actions and category-like invariants.

Contribution

It introduces a novel characterization of topological invariants for aspherical spaces via the A-genus, linking subgroup inclusions and group actions.

Findings

Characterization of sectional category using A-genus.

Analysis of sequential topological complexity in aspherical spaces.

Discussion of new category-like invariants for proper group actions.

Abstract

In this paper we characterize the sectional category of subgroup inclusions and the $r^{th}$-sequential topological complexity of aspherical spaces of a group G in terms of the A-genus in the sense of Clapp-Puppe and Bartsch for a suitable one-element family of G-spaces A, and we discuss some of the consequences of such characterization, including new ideas about notions of category-like invariants with respect to proper actions of groups.